how to make constant, looping animation?
Ok there are multiple reasons why this could be happening.
The first one is: You dont have linear interpolation
The fix for that is:


Go into the Graph Editor
Press V and select Vector


The second one is: your animation ends on the wrong frame or starts at the wrong frame. Make sure your last keyframe which is the same as the first one is never actually shown (or the other way round), because when it is, you have 2 exactly equal frames played in sequence. In practice that means you have to either put your first keyframe at frame 0 and start on the frame 1 and end at the last keyframe. Or you put your start and first keyframe on frame 1 and set the end to be 1 frame before the last keyframe.